Problem: Simplify the following expression: ${2(2k+19)-6(4-k)}$
Solution: Distribute the ${2}$ into the first set of parentheses: $ {2(}\gray{2k+19}{)} - 6(4-k) $ $ {4k+38} - 6(4-k) $ Distribute the ${-6}$ into the parentheses: $ 4k+38 {-6(}\gray{4-k}{)} $ $ 4k+38 {-24+6k} $ Rewrite the expression to group the ${k}$ terms and numeric terms: $ {4k + 6k} + {38 - 24}$ Combine the ${k}$ terms: $ {10k} + {38 - 24}$ Combine the numeric terms: $ {10k} + {14}$ The simplified expression is $10k+14$